Finite Group Databasebeta

← C127×#9469 #44573142

Subgroups — C127×#9469 #44573142

Order 32512.

578 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2972C211yesmaximal, characteristic
2C127×#2487C211yesmaximal, characteristic
3C127×#1824C212yesmaximal, complemented
4C127×#1799C211yesmaximal, characteristic
5C127×#1289C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8C8×D4×C127—24no—
9#431×C127—21no—
10C2×#99×C127—21no—
11C2×C22⋊C8×C127—21no—
12C2×C22⋊C8×C127C2212yes—
13#400×C127C412yescomplemented
14#399×C127C412yescomplemented
15#389×C127—21no—
16#386×C127—21no—
17#385×C127—21no—
18#380×C127—21no—
19#380×C127C2212yes—
20#380×C127C2211yescharacteristic
21#342×C127—21no—
22#340×C127—24no—
23C22×D4×C127D411yescharacteristic
24C23×C4×C127—21no—
25C23×C4×C127D411yescharacteristic
26C23×C4×C127C2311yescharacteristic
27C22×C8×C127—22no—
28C22×C8×C127D414yes—
29C4×D4×C127—22no—
30C4×D4×C127—22no—
31C2×C4⋊C4×C127—22no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127C2×C412yes—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—22no—
46#99×C127—42no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50C4×C8×C127—22no—
51#95×C127—22no—
52#95×C127—22no—
53#95×C127—22no—
54#95×C127C2×C412yes—
55C24×C127C22⋊C411yescharacteristic
56C24×C127C2×D411yescharacteristic
57C2×D4×C127—22no—
58C2×D4×C127—22no—
59C2×D4×C127SD1612yes—
60C2×D4×C127Q1612yes—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—42no—
66C22×C4×C127—42no—
67C22×C4×C127—42no—
68C22×C4×C127—42no—
69C22×C4×C127—82no—
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D412yes—
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127#4112yes—
77C2×C8×C127—24no—
78C2×C8×C127—44no—
79C2×C8×C127—82no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—24no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—44no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—82no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—82no—
93C42×C127—21no—
94C42×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127#10312yes—
102C23×C127C2×C22⋊C411yescharacteristic
103C23×C127#12112yes—
104C23×C127C2×SD1611yescharacteristic
105C23×C127C2×Q1611yescharacteristic
106C23×C127#13512yes—
107D4×C127—24no—
108D4×C127—24no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—24no—
112C2×C4×C127—22no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—41no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—42no—
126C2×C4×C127—81no—
127C2×C4×C127—84no—
128C2×C4×C127—82no—
129C2×C4×C127—82no—
130C2×C4×C127—82no—
131C2×C4×C127#10312yes—
132C2×C4×C127C4×D412yes—
133C2×C4×C127#12011yescharacteristic
134C2×C4×C127#12311yescharacteristic
135C8×C127—44no—
136C22×C127—21no—
137C22×C127—22no—
138C22×C127—21no—
139C22×C127—22no—
140C22×C127—22no—
141C22×C127—41no—
142C22×C127—41no—
143C22×C127—42no—
144C22×C127—42no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—81no—
148C22×C127#38611yescharacteristic
149C22×C127C2×#10311yescharacteristic
150C22×C127#41611yescharacteristic
151C22×C127#46512yes—
152C22×C127#46712yes—
153C4×C127—21no—
154C4×C127—22no—
155C4×C127—22no—
156C4×C127—41no—
157C4×C127—41no—
158C4×C127—82no—
159C4×C127—82no—
160C4×C127—162no—
161C4×C127#45812yes—
162#9469C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127—21no—
164C2×C127—22no—
165C2×C127—21no—
166C2×C127—22no—
167C2×C127—42no—
168C2×C127#189011yescharacteristic
169C2×C127#189211yescharacteristic
170C2×C127#191011yescharacteristic
171#2972C2×C12711yescharacteristic
172#2487C2×C12711yescharacteristic
173#1824C2×C12712yescomplemented
174#1799C2×C12711yescharacteristic
175#1289C2×C12712yescomplemented
176C127#946911yescharacteristic, direct product factor, Sylow
177C2×C4×D4C22×C12711yescharacteristic
178C22×C4⋊C4C22×C12711yescharacteristic
179C8×D4—24no—
180#431—21no—
181C2×#99—21no—
182C2×C22⋊C8—21no—
183C2×C22⋊C8C22×C12712yes—
184#400C4×C12712yescomplemented
185#399C4×C12712yescomplemented
186#389—21no—
187#386—21no—
188#385—21no—
189#380—21no—
190#380C22×C12712yes—
191#380C22×C12711yescharacteristic
192#342—21no—
193#340—24no—
194C22×D4D4×C12711yescharacteristic
195C23×C4—21no—
196C23×C4D4×C12711yescharacteristic
197C23×C4C23×C12711yescharacteristic
198C22×C8—22no—
199C22×C8D4×C12714yes—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C2×C4×C12712yes—
209C2×C4⋊C4C2×C4×C12711yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4C2×C4×C12711yescharacteristic
214C2×C22⋊C4D4×C12711yescharacteristic
215C2×C42D4×C12711yescharacteristic
216C4⋊C8—22no—
217#99—42no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221C4×C8—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95C2×C4×C12712yes—
226C24C22⋊C4×C12711yescharacteristic
227C24C2×D4×C12711yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4SD16×C12712yes—
231C2×D4Q16×C12712yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—82no—
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4C22⋊C4×C12711yescharacteristic
244C22×C4C22×C4×C12711yescharacteristic
245C22×C4C2×D4×C12712yes—
246C22×C4C2×D4×C12711yescharacteristic
247C22×C4#41×C12712yes—
248C2×C8—24no—
249C2×C8—44no—
250C2×C8—82no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—82no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—82no—
264C42—21no—
265C42—21no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23#103×C12712yes—
273C23C2×C22⋊C4×C12711yescharacteristic
274C23#121×C12712yes—
275C23C2×SD16×C12711yescharacteristic
276C23C2×Q16×C12711yescharacteristic
277C23#135×C12712yes—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—84no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4#103×C12712yes—
303C2×C4C4×D4×C12712yes—
304C2×C4#120×C12711yescharacteristic
305C2×C4#123×C12711yescharacteristic
306C8—44no—
307C22—21no—
308C22—22no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22#386×C12711yescharacteristic
320C22C2×#103×C12711yescharacteristic
321C22#416×C12711yescharacteristic
322C22#465×C12712yes—
323C22#467×C12712yes—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—82no—
330C4—82no—
331C4—162no—
332C4#458×C12712yes—
333C2—21no—
334C2—22no—
335C2—21no—
336C2—22no—
337C2—42no—
338C2C127×#189011yescharacteristic
339C2C127×#189211yescharacteristic
340C2C127×#191011yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C127×#1824C2semidirect
5. C127×#1289C2semidirect
13. #400×C127C4semidirect
14. #399×C127C4semidirect
162. #9469C127direct (N × H)
173. #1824C2×C127semidirect
175. #1289C2×C127semidirect
176. C127#9469direct (N × H)
184. #400C4×C127semidirect
185. #399C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#29722
C127×#24872
C127×#18242
C127×#17992
C127×#12892
#9469127